Finite Group Databasebeta

← #14302898

Subgroups — #14302898

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754609C211yesmaximal, characteristic
2#11754515C211yesmaximal, characteristic, complemented
3C2×#91107C211yesmaximal, characteristic, complemented
4C3×#65428C211yesmaximal, characteristic, complemented
5#11748421C211yesmaximal, characteristic, complemented
6C5×#4557C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10599498—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16#91572—22no—
17#91561—22no—
18#91458C412yescomplemented
19#91450—22no—
20#91428—22no—
21#91418—22no—
22#91374C412yescomplemented
23#91107—22no—
24C3×#3957—22no—
25#90977—22no—
26#70408—51nomaximal, Hall
27#65859—31no—
28#65855—31no—
29#65428D311yescharacteristic, complemented
30C2×#3955—31no—
31#65294—31no—
32C5×H(3,ℤ/4)—31no—
33#64751—31no—
34C23×D15D412yes—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60C2×C412yes—
41C2×D60D412yes—
42C2×C3×C22⋊D5—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C2×C3×D20C2×C411yescharacteristic, complemented
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic, complemented
50C2×#1202—24no—
51C2×#1200—24no—
52C3×C5×M16—21no—
53C3×C5×M16—21no—
54C2×C3×C5×C8—21no—
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×#217—21no—
59C5×#217—21no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3—21no—
62C4×C5×Dic3C2×C412yescomplemented
63C4×C5×Dic3D412yescomplemented
64C3×C22⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5D412yescomplemented
67#6667—24no—
68#6667—24no—
69#5830—51no—
70#5521—51no—
71C3×#421—51no—
72#5236—51no—
73C2×#823—51no—
74#4557D511yescharacteristic, complemented
75#4531—51no—
76C2×#709C2×D311yescharacteristic
77C22×D20—31no—
78C2×C5×M16C2×D311yescharacteristic
79C5×#117—31no—
80C5×#117—31no—
81#4072C2×D311yescharacteristic
82C2×#681—31no—
83#4041—62no—
84#4039—62no—
85#4028—62no—
86D5×C22⋊C4—62no—
87#4021—32no—
88#4020—32no—
89C4×D20—62no—
90#3957—22no—
91#3955—62no—
92#3937—62no—
93#1911—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—22no—
96C22×D15—22no—
97C22×D15—82no—
98C22×D15C22⋊C414yes—
99C22×C3×D5—21no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106D60—22no—
107D60—22no—
108D60—22no—
109D60—22no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—22no—
112C3×C22⋊D5—41no—
113C3×C22⋊D5—41no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—22no—
116C3×D20—21no—
117C3×D20—21no—
118C3×C4×D5—41no—
119C3×C4×D5—41no—
120C3×Dic10—21no—
121C3×Dic10—21no—
122#1202—84no—
123#1200—84no—
124C3×C5×C8—41no—
125C3⋊#168—41no—
126C2×C3×#41—51no—
127C22×D12—51no—
128C2×C3×M16C2×D511yescharacteristic
129C3×#117—51no—
130#947—52no—
131#940—52no—
132#937—102no—
133#930—102no—
134#926C2×D511yescharacteristic
135#926C2×D511yescharacteristic
136C2×#208—51no—
137#893—102no—
138D3×C22⋊C4—102no—
139C4×D12—102no—
140C3×#104—102no—
141#837—102no—
142#823—102no—
143C23×D5—32no—
144C22×C4×C5C22×D311yescharacteristic
145C2×C22⋊D5—21no—
146#709—21no—
147#709—21no—
148#709—21no—
149#709—21no—
150C2×D20—32no—
151C2×D20—32no—
152C2×D20—61no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20—61no—
156C2×D20—64no—
157C2×D20C4×D311yescharacteristic, complemented
158C2×C4×D5—21no—
159C2×C4×D5—64no—
160C2×Dic10C4×D311yescharacteristic, complemented
161C5×M16—21no—
162C5×M16—21no—
163C2×C5×C8—21no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C5×C22⋊C4—61no—
167C5×C22⋊C4—61no—
168C42×C5—32no—
169C42×C5—32no—
170C22⋊Dic5—21no—
171#685—64no—
172#685—64no—
173C4⋊Dic5—21no—
174C4×Dic5#6712yescomplemented
175#681—61no—
176#681—61no—
177C2×#168—61no—
178#535—151no—
179#518—151no—
180#421—51no—
181#421—151no—
182C2×#100—151no—
183H(3,ℤ/4)—31no—
184H(3,ℤ/4)—151no—
185C22×C3×C5—41no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#12011yescharacteristic
188C22×C3×C5#12311yescharacteristic
189C2×D15—24no—
190C2×D15—44no—
191C2×D15—44no—
192C2×D15—82no—
193C2×C3×D5—42no—
194C2×C3×D5—41no—
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×Dic5—42no—
200C3×Dic5—41no—
201C5×Dic3—42no—
202C5×Dic3—42no—
203C23×D3—52no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C3×#41—101no—
208C2×C3×Q8—51no—
209C2×C3×D4—51no—
210C2×C3×D4—101no—
211C22×C3×C4—101no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—104no—
214C2×D12—52no—
215C2×D12—52no—
216C2×D12—101no—
217C2×D12—101no—
218C2×D12—101no—
219C2×D12—101no—
220C2×C4×D3—104no—
221C3×M16—21no—
222C3×M16—21no—
223C2×C3×C8—21no—
224C3×C4⋊C4—101no—
225C3×C22⋊C4—101no—
226C3×C42—52no—
227#217—21no—
228#217—21no—
229(C2×D3)⋊C4—104no—
230(C2×D3)⋊C4—104no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4×Dic3C4×D512yescomplemented
234C4×Dic3D2012yescomplemented
235#208—101no—
236#208—101no—
237C2×C3⋊C8—101no—
238C23×C5D3×D411yescharacteristic
239C22×D5—21no—
240C22×D5—34no—
241C22×D5—62no—
242C22×D5—62no—
243C22×D5—242no—
244C2×C4×C5—62no—
245C2×C4×C5—62no—
246C2×C4×C5C2×C4×D311yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C22⋊D5—41no—
253C22⋊D5—41no—
254C2×Dic5—21no—
255C2×Dic5—22no—
256D20—21no—
257D20—21no—
258D20—62no—
259D20—62no—
260D20—62no—
261D20—62no—
262D20—244no—
263C4×D5—41no—
264C4×D5—41no—
265C4×D5—244no—
266Dic10—21no—
267Dic10—21no—
268C5×C8—41no—
269#168—121no—
270C2×#41—51no—
271C22×D4—151no—
272C2×M16—151no—
273C2×M16D3×D511yescharacteristic
274#127—152no—
275#124—152no—
276#121—302no—
277#120—302no—
278C4×D4—302no—
279C4×D4—302no—
280#117—31no—
281#117—31no—
282#117—51no—
283C2×C22⋊C4—302no—
284#104—102no—
285#104—302no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—44no—
292C3×D5—81no—
293C23×C3—101no—
294C23×C3D4×D511yescharacteristic
295C22×D3—54no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—402no—
299C3×Q8—101no—
300C3×Q8—101no—
301C3×D4—101no—
302C3×D4—101no—
303C3×D4—201no—
304C3×D4—201no—
305C2×C3×C4—101no—
306C2×C3×C4—102no—
307C2×C3×C4—201no—
308C2×C3×C4—201no—
309C2×C3×C4C2×C4×D511yescharacteristic
310C2×C3×C4C2×D2011yescharacteristic
311C2×C3×C4#70911yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4#71311yescharacteristic
315#67—404no—
316C2×Dic3—22no—
317C2×Dic3—22no—
318D12—102no—
319D12—102no—
320D12—102no—
321D12—102no—
322C4×D3—404no—
323C3×C8—41no—
324C3⋊C8—201no—
325C22×C5—41no—
326C22×C5D3×C22⋊C411yescharacteristic
327C22×C5#88311yescharacteristic
328C22×C5#93711yescharacteristic
329C2×D5—42no—
330C2×D5—41no—
331C2×D5—64no—
332C2×D5—124no—
333C2×D5—124no—
334C2×D5—242no—
335C4×C5—122no—
336C4×C5—122no—
337C4×C5#67⋊C411yescharacteristic
338C4×C5#88411yescharacteristic
339C4×C5C4×#6711yescharacteristic
340C4×C5#93811yescharacteristic
341Dic5—42no—
342Dic5—41no—
343C24—152no—
344#41—101no—
345#41—101no—
346#41—101no—
347#41—101no—
348C2×Q8—51no—
349C2×D4—51no—
350C2×D4—101no—
351C2×D4—152no—
352C2×D4—152no—
353C2×D4—304no—
354C2×D4—301no—
355C2×D4—301no—
356C2×D4—301no—
357C2×D4—301no—
358C22×C4—101no—
359C22×C4—304no—
360C22×C4C2×D3×D511yescharacteristic
361M16—21no—
362M16—21no—
363M16—301no—
364M16—301no—
365C2×C8—21no—
366C2×C8—301no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—101no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—101no—
373C22⋊C4—304no—
374C22⋊C4—304no—
375C42—32no—
376C42—32no—
377C42—52no—
378C3×C5#191111yescharacteristic, complemented, Hall
379C22×C3—41no—
380C22×C3—202no—
381C22×C3—201no—
382C22×C3D5×C22⋊C411yescharacteristic
383C22×C3#402811yescharacteristic
384C22×C3#404011yescharacteristic
385C2×D3—104no—
386C2×D3—204no—
387C2×D3—204no—
388C2×D3—402no—
389C3×C4—202no—
390C3×C4—201no—
391C3×C4C4×D2011yescharacteristic
392C3×C4#403011yescharacteristic
393C3×C4#403911yescharacteristic
394C3×C4#404111yescharacteristic
395Dic3—42no—
396Dic3—42no—
397C2×C5—21no—
398C2×C5—21no—
399C2×C5—21no—
400C2×C5#495611yescharacteristic
401D5—81no—
402D5—124no—
403C23—101no—
404C23—154no—
405C23—302no—
406C23—302no—
407C23—1202no—
408C23#677711yescharacteristic
409Q8—101no—
410Q8—101no—
411D4—101no—
412D4—101no—
413D4—201no—
414D4—201no—
415D4—302no—
416D4—302no—
417D4—302no—
418D4—302no—
419D4—1204no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—101no—
423C2×C4—102no—
424C2×C4—201no—
425C2×C4—201no—
426C2×C4—1204no—
427C2×C4#677311yescharacteristic
428C2×C4C4×D3×D511yescharacteristic
429C2×C4D3×D2011yescharacteristic
430C2×C4#677911yescharacteristic
431C2×C4D5×#6711yescharacteristic
432C2×C4#679011yescharacteristic
433C8—41no—
434C8—601no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—401no—
439C2×C3#6495411yescharacteristic
440D3—204no—
441C5#7040811yescharacteristic, complemented, Sylow
442C22—41no—
443C22—202no—
444C22—201no—
445C22—304no—
446C22—604no—
447C22—604no—
448C22—1202no—
449C22#9135611yescharacteristic
450C22#9147311yescharacteristic
451C22#9147411yescharacteristic
452C4—122no—
453C4—122no—
454C4—202no—
455C4—201no—
456C4#9139511yescharacteristic
457C4#9144411yescharacteristic
458C4#9145911yescharacteristic
459C4#9153311yescharacteristic
460C3#1059949811yescharacteristic, complemented, Sylow
461C2—21no—
462C2—21no—
463C2—21no—
464C2—401no—
465C2—604no—
466C2#1174870011yescharacteristic
subgroupG/H
centerC2#11748700
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754609C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1911
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11754515C2semidirect
3. C2×#91107C2semidirect
4. C3×#65428C2semidirect
5. #11748421C2semidirect
6. C5×#4557C2semidirect
7. #11745969C2semidirect
18. #91458C4semidirect
22. #91374C4semidirect
29. #65428D3semidirect
47. C2×C3×D20C2×C4semidirect
49. C2×C3×Dic10C2×C4semidirect
62. C4×C5×Dic3C2×C4semidirect
63. C4×C5×Dic3D4semidirect
66. C3×C4×Dic5D4semidirect
74. #4557D5semidirect
157. C2×D20C4×D3semidirect
160. C2×Dic10C4×D3semidirect
174. C4×Dic5#67semidirect
233. C4×Dic3C4×D5semidirect
234. C4×Dic3D20semidirect
378. C3×C5#1911semidirect
441. C5#70408semidirect
460. C3#10599498semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117546092
#117545152
C2×#911072
C3×#654282
#117484212
C5×#45572
#117459692
#105994983
#704085